Table X-P
Internal Similitude Centers.
Points available at the Kimberling's Encyclopedia ETC.
The ETC version: The 8998 points version of 2015.
The "Discoverer" database version: October 2013.
Last update: 2016-04-18

      Kimberling Notation     Role  
  1     X(1) Incenter     Internal Center of Similitude of the Circumcircle of the Johnson Triangle and the Outer Johnson-Yff Circle  
  2     X(2) Centroid     Internal Center of Similitude of the Nine-Point Circle of the Johnson Triangle and the Circumcircle  
  3     X(3) Circumcenter     Internal Center of Similitude of the Antimedial Circle of the Johnson Triangle and the Circumcircle  
  4     X(3) Circumcenter     Internal Center of Similitude of the Antimedial Circle of the Johnson Triangle and the Second Brocard Circle  
  5     X(4) Orthocenter     Internal Center of Similitude of the Circumcircle of the Johnson Triangle and the Antimedial Circle  
  6     X(4) Orthocenter     Internal Center of Similitude of the Second Brocard Circle of the Johnson Triangle and the Antimedial Circle  
  7     X(5) Nine-Point Center     Internal Center of Similitude of the Circumcircle of the Johnson Triangle and the Circumcircle  
  8     X(5) Nine-Point Center     Internal Center of Similitude of the Incircle of the Johnson Triangle and the Incircle  
  9     X(5) Nine-Point Center     Internal Center of Similitude of the Incentral Circle of the Johnson Triangle and the Incentral Circle  
  10     X(5) Nine-Point Center     Internal Center of Similitude of the Symmedial Circle of the Johnson Triangle and the Symmedial Circle  
  11     X(5) Nine-Point Center     Internal Center of Similitude of the Extouch Circle of the Johnson Triangle and the Extouch Circle  
  12     X(5) Nine-Point Center     Internal Center of Similitude of the Excentral Circle of the Johnson Triangle and the Excentral Circle  
  13     X(5) Nine-Point Center     Internal Center of Similitude of the Antimedial Circle of the Johnson Triangle and the Antimedial Circle  
  14     X(5) Nine-Point Center     Internal Center of Similitude of the Tangential Circle of the Johnson Triangle and the Tangential Circle  
  15     X(5) Nine-Point Center     Internal Center of Similitude of the Spieker Circle of the Johnson Triangle and the Spieker Circle  
  16     X(5) Nine-Point Center     Internal Center of Similitude of the Adams Circle of the Johnson Triangle and the Adams Circle  
  17     X(5) Nine-Point Center     Internal Center of Similitude of the Conway Circle of the Johnson Triangle and the Conway Circle  
  18     X(5) Nine-Point Center     Internal Center of Similitude of the Brocard Circle of the Johnson Triangle and the Brocard Circle  
  19     X(5) Nine-Point Center     Internal Center of Similitude of the Second Brocard Circle of the Johnson Triangle and the Second Brocard Circle  
  20     X(5) Nine-Point Center     Internal Center of Similitude of the Orthocentroidal Circle of the Johnson Triangle and the Orthocentroidal Circle  
  21     X(5) Nine-Point Center     Internal Center of Similitude of the Lester Circle of the Johnson Triangle and the Lester Circle  
  22     X(5) Nine-Point Center     Internal Center of Similitude of the Inner Johnson-Yff Circle of the Johnson Triangle and the Inner Johnson-Yff Circle  
  23     X(5) Nine-Point Center     Internal Center of Similitude of the Outer Johnson-Yff Circle of the Johnson Triangle and the Outer Johnson-Yff Circle  
  24     X(5) Nine-Point Center     Internal Center of Similitude of the Lemoine Circle of the Johnson Triangle and the Lemoine Circle  
  25     X(5) Nine-Point Center     Internal Center of Similitude of the Gallatly Circle of the Johnson Triangle and the Gallatly Circle  
  26     X(5) Nine-Point Center     Internal Center of Similitude of the Kenmotu Circle of the Johnson Triangle and the Kenmotu Circle  
  27     X(5) Nine-Point Center     Internal Center of Similitude of the Cosine Circle of the Johnson Triangle and the Cosine Circle  
  28     X(5) Nine-Point Center     Internal Center of Similitude of the Apollonius Circle of the Johnson Triangle and the Apollonius Circle  
  29     X(5) Nine-Point Center     Internal Center of Similitude of the Taylor Circle of the Johnson Triangle and the Taylor Circle  
  30     X(10) Spieker Center     Internal Center of Similitude of the Nine-Point Circle of the Johnson Triangle and the Apollonius Circle  
  31     X(12) Feuerbach Perspector     Internal Center of Similitude of the Nine-Point Circle of the Johnson Triangle and the Incircle  
  32     X(25) Product of the Orthocenter and the Symmedian Point     Internal Center of Similitude of the Nine-Point Circle of the Johnson Triangle and the Tangential Circle  
  33     X(55) Internal Center of Similitude of Circumcircle and Incircle     Internal Center of Similitude of the Nine-Point Circle of the Johnson Triangle and the Outer Johnson-Yff Circle  
  34     X(265)     Internal Center of Similitude of the Sine-Triple-Angle Circle of the Johnson Triangle and the Nine-Point Circle  
  35     X(355) Center of the Fuhrmann Circle     Internal Center of Similitude of the Outer Johnson-Yff Circle of the Johnson Triangle and the Circumcircle  
  36     X(381) Center of the Orthocentroidal Circle     Internal Center of Similitude of the Circumcircle of the Johnson Triangle and the Nine-Point Circle  
  37     X(485) Outer Vecten Point     Internal Center of Similitude of the Nine-Point Circle of the Johnson Triangle and the Cosine Circle  
  38     X(946)     Internal Center of Similitude of the Apollonius Circle of the Johnson Triangle and the Nine-Point Circle  
  39     X(1346)     Internal Center of Similitude of the Nine-Point Circle of the Johnson Triangle and the Orthocentroidal Circle  
  40     X(1348)     Internal Center of Similitude of the Nine-Point Circle of the Johnson Triangle and the Brocard Circle  
  41     X(1478) Center of the Inner Johnson-Yff Circle     Internal Center of Similitude of the Circumcircle of the Johnson Triangle and the Incircle  
  42     X(1656)     Internal Center of Similitude of the Antimedial Circle of the Johnson Triangle and the Nine-Point Circle  
  43     X(1676) Outer Kiepert omega/2 Point     Internal Center of Similitude of the Nine-Point Circle of the Johnson Triangle and the Lemoine Circle  
  44     X(1698)     Internal Center of Similitude of the Nine-Point Circle of the Johnson Triangle and the Excentral Circle  
  45     X(2009)     Internal Center of Similitude of the Nine-Point Circle of the Johnson Triangle and the Gallatly Circle  
  46     X(2070)     Internal Center of Similitude of the Antimedial Circle of the Johnson Triangle and the Tangential Circle  
  47     X(2566)     Internal Center of Similitude of the Nine-Point Circle of the Johnson Triangle and the Second Brocard Circle  
  48     X(2886)     Internal Center of Similitude of the Nine-Point Circle of the Johnson Triangle and the Spieker Circle  
  49     X(3070)     Internal Center of Similitude of the Circumcircle of the Johnson Triangle and the Cosine Circle  
  50     X(3091)     Internal Center of Similitude of the Nine-Point Circle of the Johnson Triangle and the Antimedial Circle  
  51     X(3153)     Internal Center of Similitude of the Tangential Circle of the Johnson Triangle and the Antimedial Circle  
  52     X(3295)     Internal Center of Similitude of the Antimedial Circle of the Johnson Triangle and the Incircle  
  53     X(3311)     Internal Center of Similitude of the Antimedial Circle of the Johnson Triangle and the Cosine Circle  
  54     X(3373) Outer Kiepert PI/8 Point     Internal Center of Similitude of the Nine-Point Circle of the Johnson Triangle and the Kenmotu Circle  
  55     X(3560)     Internal Center of Similitude of the Inner Johnson-Yff Circle of the Johnson Triangle and the Incircle  
  56     X(3579)     Internal Center of Similitude of the Antimedial Circle of the Johnson Triangle and the Excentral Circle  
  57     X(3585)     Internal Center of Similitude of the Circumcircle of the Johnson Triangle and the Inner Johnson-Yff Circle  
  58     X(5587)     Internal Center of Similitude of the Circumcircle of the Johnson Triangle and the Excentral Circle  
  59     X(5603)     Internal Center of Similitude of the Spieker Circle of the Johnson Triangle and the Incircle  
  60     X(5720)     Internal Center of Similitude of the Outer Johnson-Yff Circle of the Johnson Triangle and the Excentral Circle  
  61     X(5722)     Internal Center of Similitude of the Excentral Circle of the Johnson Triangle and the Outer Johnson-Yff Circle  
  62     X(5790)     Internal Center of Similitude of the Incircle of the Johnson Triangle and the Spieker Circle  
  63     X(5886)     Internal Center of Similitude of the Excentral Circle of the Johnson Triangle and the Circumcircle  
  64     X(6289)     Internal Center of Similitude of the Cosine Circle of the Johnson Triangle and the Nine-Point Circle  
  65     X(6911)     Internal Center of Similitude of the Outer Johnson-Yff Circle of the Johnson Triangle and the Incircle  
  66     X(6917)     Internal Center of Similitude of the Incircle of the Johnson Triangle and the Inner Johnson-Yff Circle  
  67     X(6929)     Internal Center of Similitude of the Incircle of the Johnson Triangle and the Outer Johnson-Yff Circle  
  68     X(7330)     Internal Center of Similitude of the Incircle of the Johnson Triangle and the Excentral Circle  
  69     X(7517)     Internal Center of Similitude of the Circumcircle of the Johnson Triangle and the Tangential Circle  
  70     X(7680)     Internal Center of Similitude of the Spieker Circle of the Johnson Triangle and the Nine-Point Circle